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portada Hessenberg and Tridiagonal Matrices. Theory and Examples
Type
Physical Book
Publisher
Author
Collection
Other Titles in Applied Mathematics
Year
2025
Language
English
Pages
227
Format
Paperback
ISBN13
9781611978445

Hessenberg and Tridiagonal Matrices. Theory and Examples

Gérard Meurant (Author) · SIAM - Society for Industrial and Applied Mathematics · Paperback

Hessenberg and Tridiagonal Matrices. Theory and Examples - Gérard Meurant

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Synopsis "Hessenberg and Tridiagonal Matrices. Theory and Examples"

Explore advanced concepts for Hessenberg and tridiagonal matrices while examining determinants, LU factorizations, inverses, and eigenvalues through practical examples and numerical experiments. It also addresses unitary forms and inverse eigenvalue challenges, engaging applied mathematicians, physicists, and engineers alike.

This is the only book devoted exclusively to Hessenberg and tridiagonal matrices. Hessenberg matrices are involved in Krylov methods for solving linear systems or computing eigenvalues and eigenvectors, in the QR algorithm for computing eigenvalues, and in many other areas of scientific computing (for instance, control theory). Matrices that are both upper and lower Hessenberg are tridiagonal. Their entries are zero except for the main diagonal and the subdiagonal and updiagonal next to it.

Hessenberg and Tridiagonal Matrices: Theory and Examples presents known and new results; describes the theoretical properties of the matrices, their determinants, LU factorizations, inverses, and eigenvalues; illustrates the theoretical properties with applications and examples as well as numerical experiments; and considers unitary Hessenberg matrices, inverse eigenvalue problems, and Toeplitz tridiagonal matrices.

Audience
This book is intended for applied mathematicians, especially those interested in numerical linear algebra, and it will also be of interest to physicists and engineers.

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